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Theorem sscoll2 13216
 Description: Version of ax-sscoll 13215 with two disjoint variable conditions removed and without initial universal quantifiers. (Contributed by BJ, 5-Oct-2019.)
Assertion
Ref Expression
sscoll2
Distinct variable groups:   ,,,,,,   ,,
Allowed substitution hints:   (,,,,)

Proof of Theorem sscoll2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 nfv 1508 . . 3
2 nfv 1508 . . . 4
3 simpl 108 . . . . . 6
4 rexeq 2627 . . . . . . 7
54adantl 275 . . . . . 6
63, 5raleqbidv 2638 . . . . 5
7 nfv 1508 . . . . . 6
8 nfv 1508 . . . . . . 7
9 rexeq 2627 . . . . . . . . 9
109adantr 274 . . . . . . . 8
1110bibi2d 231 . . . . . . 7
128, 11albid 1594 . . . . . 6
137, 12rexbid 2436 . . . . 5
146, 13imbi12d 233 . . . 4
152, 14albid 1594 . . 3
161, 15exbid 1595 . 2
17 ax-sscoll 13215 . . . 4
1817spi 1516 . . 3
1918spi 1516 . 2
2016, 19ch2varv 13005 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1329  wex 1468  wral 2416  wrex 2417 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sscoll 13215 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422 This theorem is referenced by: (None)
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